Editing Reaction rate (section)

===Example of a complex reaction: hydrogen and nitric oxide===
For the reaction

<math chem display=block>\ce{2H2_{(g)}} + \ce{2NO_{(g)} -> N2_{(g)}} + \ce{2H2O_{(g)}},</math>

the observed rate equation (or rate expression) is
<math chem display=block> v = k [\ce{H2}] [\ce{NO}]^2.</math><!--Please do not change this to second order in H2. The experimental result is first order in H2. Read the section to find out why.-->

As for many reactions, the experimental rate equation does not simply reflect the stoichiometric coefficients in the overall reaction: It is [[order of reaction|third order]] overall: first order in H<sub>2</sub> and second order in NO,  even though the stoichiometric coefficients of both reactants are equal to 2.<ref>{{cite book|author-link=Keith J. Laidler|last=Laidler |first=K. J. |title=Chemical Kinetics |edition=3rd |publisher=Harper & Row |date=1987 |page=277 |isbn=0060438622}}</ref>

In chemical kinetics, the overall reaction rate is often explained using a mechanism consisting of a number of elementary steps. Not all of these steps affect the rate of reaction; normally the slowest elementary step controls the reaction rate. For this example, a possible mechanism is

<math chem display=block> \begin{array}{rll}
1) & \quad \ce{2NO_{(g)} <=> N2O2_{(g)}} & (\text{fast equilibrium}) \\
2) & \quad \ce{N2O2 + H2 -> N2O + H2O} & (\text{slow}) \\
3) & \quad \ce{N2O + H2 -> N2 + H2O} & (\text{fast}).
\end{array}</math>

Reactions 1 and 3 are very rapid compared to the second, so the slow reaction 2 is the rate-determining step. This is a [[bimolecular]] elementary reaction whose rate is given by the second-order equation
<math chem display=block> 
v = k_2 [\ce{H2}] [\ce{N2O2}] ,
</math>
where {{math|''k''<sub>2</sub>}} is the rate constant for the second step.

However N<sub>2</sub>O<sub>2</sub> is an unstable intermediate whose concentration is determined by the fact that the first step is in [[chemical equilibrium|equilibrium]], so that <math chem>\ce{[N2O2] = \mathit{K}_1[NO]^2},</math> where {{math|''K''<sub>1</sub>}} is the [[equilibrium constant]] of the first step. Substitution of this equation in the previous equation leads to a rate equation expressed in terms of the original reactants
<math chem display=block> v = k_2 K_1 [\ce{H2}] [\ce{NO}]^2 \,.</math>

This agrees with the form of the observed rate equation if it is assumed that {{math|1=''k'' = ''k''<sub>2</sub>''K''<sub>1</sub>}}. In practice the rate equation is used to suggest possible mechanisms which predict a rate equation in agreement with experiment.

The second molecule of H<sub>2</sub> does not appear in the rate equation because it reacts in the third step, which is a rapid step ''after'' the rate-determining step, so that it does not affect the overall reaction rate.